Four separate topics have been investigated here: (a) (Hill, Eisenberg). The equilibrium binding constants of the myosin fragments S-1 and HMM onto an actin filament have been calculated, semi-quantitatively, from statistical mechanical first principles. The relations between one-headed and two-headed binding are especially interesting. Agreement with experiment is quite satisfactory. (b) (Hill, Eisenberg, Greene). The experimental data of Greene and Eisenberg on the cooperative equilibrium binding of S-1-ADP onto actin-troponin-tropomyosin, in the presence and absence of Ca ions, have been matched very well by a theoretical treatment that is a rather complicated extension of the well-known two-state, linear Ising model. The experiments and the theory are being extended to allow for different salt concentrations and for different nucleotides bound to the S-1. (c) (Hill). Steady-state head-to-tail polymerization of actin or of microtubules requires a flux of ATP or of GTP, respectively. In this work, an explicit kinetic model was used to examine the bioenergetic aspects of this process. Also investigated, for an important special case, was the steady-state polymer length distribution. The distribution found is of the same form as found experimentally. (d) (Chen). In general, the structure of a covalently-closed circular DNA in solution depends on the bending and torsional stiffness of the double helix of the DNA molecule. The resistance of DNA to bending can be deduced from the experimentally determined DNA persistence length. In contrast, the torsional stiffness remains obscure. This is because the torsional stiffness does not affect any properties of linear DNA molecules. It has been reported that theoretical studies of fluctuations of writhing numbers of model ring polymers could be used to estimate the torsional stiffness of DNA molecules. A necessary step in these studies is to generate a large number of ring polymers. In this current study, we have devised an efficient method of generating ring polymers (on lattice or off lattice) based on the "dimerization" method of Alexadrowicz. The torsional stiffness of DNA molecules will be studied using the ring polymers generated by this method.